Note: Sensitivity analysis of the optimum to perturbation of the profit of a subset of items in the binary knapsack problem

Authors:
Tarik Belgacem;Mhand Hifi
Affiliations:
CES, CERMSEM, MSE, Université Paris 1, 106-112, bd de l'Hôpital, 75013 Paris, France;CES, CERMSEM, MSE, Université Paris 1, 106-112, bd de l'Hôpital, 75013 Paris, France and Université de Picardie Jules Verne, 5 rue du Moulin Neuf, 80000 Amiens, France
Venue:
Discrete Optimization
Year:
2008

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Abstract

In this paper, we study the sensitivity of the optimum of the binary knapsack problem to perturbations of the profit of a subset of items. In order to stabilize the optimal solution, two cases are distinguished. The first case represents a subset of items whose perturbation can be done individually. The second case represents a subset of items where perturbing the profit of each item requires the perturbation of the profit of the other items. We will study the impact of the results obtained on an instance of the binary knapsack problem while considering the various cases.